Hypersurfaces with parallel affine curvature tensor R*

Barbara Opozda; Leopold Verstraelen

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 1, page 25-32
  • ISSN: 0066-2216

Abstract

top
In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space ℝ n + 1 . In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

How to cite

top

Opozda, Barbara, and Verstraelen, Leopold. "Hypersurfaces with parallel affine curvature tensor R*." Annales Polonici Mathematici 72.1 (1999): 25-32. <http://eudml.org/doc/262618>.

@article{Opozda1999,
abstract = {In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^\{n+1\}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.},
author = {Opozda, Barbara, Verstraelen, Leopold},
journal = {Annales Polonici Mathematici},
keywords = {curvature tensor; induced connection; affine normal; equiaffine normal; Blaschke metric; affine curvature tensor; central quadric},
language = {eng},
number = {1},
pages = {25-32},
title = {Hypersurfaces with parallel affine curvature tensor R*},
url = {http://eudml.org/doc/262618},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Opozda, Barbara
AU - Verstraelen, Leopold
TI - Hypersurfaces with parallel affine curvature tensor R*
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 1
SP - 25
EP - 32
AB - In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^{n+1}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.
LA - eng
KW - curvature tensor; induced connection; affine normal; equiaffine normal; Blaschke metric; affine curvature tensor; central quadric
UR - http://eudml.org/doc/262618
ER -

References

top
  1. [D]₁ R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space, Results Math. 20 (1991), 600-621. Zbl0752.53009
  2. [D]₂ R. Deszcz, Certain curvature characterizations of affine hypersurfaces, Colloq. Math. 63 (1992), 21-39. Zbl0797.53005
  3. [NS] K. Nomizu and T. Sasaki, Affine Differential Geometry, Cambridge Univ. Press, 1994. 
  4. [O] B. Opozda, A class of projectively flat surfaces, Math. Z. 219 (1995), 77-92. Zbl0823.53012
  5. [OS] B. Opozda and T. Sasaki, Surfaces whose images of affine normal are curves, Kyushu Math. J. 49 (1995), 1-10. Zbl0837.53012
  6. [OV] B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, in: Geometry and Topology of Submanifolds II, World Sci., 1990, 271-293. 
  7. [VV] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105. Zbl0535.53007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.